These are standard:
F5 = copy
F6 = rename/move
To me, the rename is more misnomer than reality, but that's not the issue
here, which is that the edit the filename first process triggered by
shifting
these keys isn't the same in all environments. For years I've seen that in
X,
Shift-F5 & Shift-F6 actually do as expected. But on the virtual consoles,
I've only seen that they do that when running *ubuntu (and maybe Debian
too?). In Fedora, Mandriva & SUSE on virtual consoles, Shift-F3 is copy
with
edit destination name, and Shift-F4 is move with edit destination name. Is
there some config file option I can change to make the behavior in most
distros the same as in *ubuntu? Why is there this ubiquitous difference?

Yes - there is such a file. Kill the f11-f20 lines under the
[terminal:linux] section of mc.lib. It is most likely located
under /usr/share/mc/ or /etc/mc/.
In fact maybe there are more invalid key sequences under this
section. It might be worth removing this section or at least
verifying all the sequences for the upcoming release. In any case
f11-f20 have entries in the "linux" terminfo netry so these entries
are tottaly unjustified.
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